NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.3 Solutions 

CBSE CLASS XII Related Questions

  • 1.

    If \(y = \sqrt{\log \left\{ \sin \left( \dfrac{x^2}{3} + 1 \right) \right\}}\), then show that

    \[ \frac{dy}{dx} = \frac{x \cot \left( \dfrac{x^2}{3} + 1 \right)}{3y}. \]


      • 2.

        Differential of \( \log \sin x \) with respect to \( \sqrt{\cos x} \) is :

          • \( -2\sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
          • \( \sqrt{\cos x}\cdot\cot x\cdot\operatorname{cosec} x \)
          • \( \frac{2\sqrt{\cos x}}{\sin x} \)
          • \( \frac{1}{\sin x\sqrt{\cos x}} \)

        • 3.

          For the following Linear Programming Problem, shade the feasible region on the graph and find the coordinates of its corner points :

          Minimize \(Z = 18x + 10y\)

          subject to constraints

          \[ \begin{aligned} 4x + y &\ge 20 \\ 2x + 3y &\ge 30 \\ x, y &\ge 0. \end{aligned} \]


            • 4.

              If \(P(A) = 0.3\), \(P(B) = 0.7\) and \(P(B/A) = 0.5\), then \(P(A \cup B)\) is :

                • \(0.35\)
                • \(0.85\)
                • \(0.5\)
                • \(0.21\)

              • 5.

                Find the product of the maximum and minimum values of the function \( f(x) = \cos x - \frac{1}{2}\cos 2x,\ x \in \left[0, \frac{\pi}{2}\right] \).


                  • 6.

                    Evaluate :

                    \[ I = \int_{-\pi}^{\pi} \frac{2x\,(1+\sin x)}{1+\cos^2 x}\,dx \]

                      CBSE CLASS XII Previous Year Papers

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